2 citations · 2 across the 5 of their papers we have counts for
8 papers
Modeling Combinatorial Disjunctive Constraints via Junction Trees
Bochuan Lyu, Illya V. Hicks, Joey Huchette
We introduce techniques to build small ideal mixed-integer programming (MIP) formulations of combinatorial disjunctive constraints (CDCs) via the independent branching scheme. We p…
Optimal Sensor Placement in Power Grids: Power Domination, Set Covering, and the Neighborhoods of Zero Forcing Forts
Logan A. Smith, Illya V. Hicks
To monitor electrical activity throughout the power grid and mitigate outages, sensors known as phasor measurement units can installed. Due to implementation costs, it is desirable…
An integer program and new lower bounds for computing the strong rainbow connection numbers of graphs
Logan A. Smith, David T. Mildebrath, Illya V. Hicks
We present an integer programming model to compute the strong rainbow connection number, , of any simple graph . We introduce several enhancements to the proposed model,…
A Polynomial Time Algorithm for Computing the Strong Rainbow Connection Numbers of Odd Cacti
Logan A. Smith, David T. Mildebrath, Illya V. Hicks
We consider the problem of computing the strong rainbow connection number for cactus graphs in which all cycles have odd length. We present a formula to calculate $src…
Power domination throttling
Boris Brimkov, Joshua Carlson, Illya V. Hicks +2
A power dominating set of a graph is a set that colors every vertex of according to the following rules: in the first timestep, every vertex in be…
Graphs with Extremal Connected Forcing Numbers
Boris Brimkov, Caleb C. Fast, Illya V. Hicks
Zero forcing is an iterative graph coloring process where at each discrete time step, a colored vertex with a single uncolored neighbor forces that neighbor to become colored. The…